People are very curious about Terry Wogan. Specifically, they are curious about his hair. 'Come on,' they whisper. 'It's got to be a wig.' A few days ago, when I first discovered that I was going to meet him, I dismissed this kind of talk, among my own friends at least, with a stern click of my tongue. Forget the thatch, I said. Wogan is a Light Entertainment Genius, a gentle humourist in the tradition of his idols Thurber and Perelman, and you'd do well to treasure him while his wonderful waffly warble - a sort of absurdist stream of consciousness - can still be heard on our airwaves. Oh dear. Now he's sitting opposite me, I feel quite embarrassed by this. My friends, it turns out, were right. The hair is absolutely captivating, every bit as darling as last season's fur tippets. It's all I can do not to reach over and stroke it.

We are drinking coffee in a hotel in what used to be County Hall, on the south bank of the Thames. Wogan has hot-footed it here straight from the studio of his Channel Five chatshow, the very last edition of which was broadcast on Friday (another failure for Chris Evans, whose company was behind it). Tomato of face and darty of eye, he is dressed in high-Tarby style: baby blue blazer, slip-on shoes and novelty tie featuring a cartoon of a fox chasing a chicken.

It is the hair, though, that is his, well, crowning glory. I am certain it is not a wig (for one thing, it is convincingly threaded with grey; for another, it doesn't cover the bald patch at the back of his head). Then again, neither have I seen its like before. At the grand old age of 65, Wogan is in possession of a hedge so wildly exuberant there could be three songbirds and an old tramp living in it.

It takes him a while to settle down and listen to my questions; at first, he just chunters away, willy-nilly. In part, this is probably because there is still adrenaline chugging around his roly-poly body. But mostly, I think, he is just so used to hamming it up as the public Terry Wogan - a daffy, self-deprecating chap who imagines he has only just jumped off the boat from Ireland - that he is almost incapable of playing the real Terry Wogan. Joke follows joke, and he is the butt of them all.

Why is his Radio 2 breakfast show so amazingly successful? 'People make a decision: they want news or music or wall-to-wall rubbish. In my case, it's wall-to-wall rubbish.' What is the secret of his staying power? 'People confuse longevity with merit. Look at Cliff Richard.' What is he doing later? 'I'm sorry. I can't tell you that.' This last is deadpan but then, as ever, an endearing titter somehow escapes his beetroot lips. 'Hee, hee. You're obviously trying to find out if I have a mistress.'

He has taken the axing of The Terry and Gaby Show (his co-presenter was Gaby Roslin) in his stride. After all, he has been here before; in 1992, he lost his thrice-weekly BBC1 chatshow in similar fashion. Moreover, he is older now, and already gets up at 5.30 every morning to do Wake Up to Wogan. 'It's finished, that's all,' he says. 'It's a pity. In my humble and unbiased opinion, it's a terrific show. On the other hand, the old bones are creaking.'

Lately, he admits, his thoughts have - whisper it softly - been turning to retirement. His contract at the BBC, where eight million devoted listeners tune in to him each weekday, runs only until next March. 'Will I have the guts to retire? What you have to avoid is leaving with a bad taste, hanging on too long. But what is too long?'

He worries that, were he to give it all up, he might annoy Helen, his wife of 39 years. 'She has developed a social life of her own. She's better than I am socially. In my job, you work with three people. You don't get to build up a whole new set of friends. I don't think she'd welcome my stopping at home.' A pause, then another wheezy chuckle. 'But the BBC air conditioning is not good for your health. If you don't come out with legionnaire's disease, you're extremely lucky.'

Still, he has the luxury of being able to pontificate about such matters in public because, however pathological his desire to make light of his abilities ('I just found something I could do,' he insists), there is a dearth of talent in radio and TV right now. Wogan, a broadcaster of consummate brilliance, is a precious commodity, a 22-carat performer in a world of fool's gold. Has he noticed any talent coming up behind him? Apparently not. 'I like Jonathan Ross,' he says. 'Ant and Dec are great little fellas. But there are a lot of people - I won't name names - who you think: why have they been given a long-term contract? They buy up people who've made it on a minor channel and expect them to make it on a major channel.' He looks momentarily glum. 'You hope that people will emerge but it's so difficult to produce anything popular nowadays. Universal appeal is a thing of the past.' By now, I am ready for the ironic pay-off line. 'I mean, not even the Eurovision Song Contest is watched by everybody.'

Terry Wogan was born in Limerick, where his father ran a grocer's shop. He has one brother, who is six years younger than him. 'My parents were shy people and the worst sin in the Catholic church, after sex, was vanity. So how any of us came out of it with any self-regard, I don't know. But I always had self-esteem. I think it came from being on my own for so long before my brother was born.' But the Limerick of his childhood was 'cursed' with religion and not even the scepticism of his parents - 'They knew it was a lot of rubbish' - could entirely protect him from it.

'There were hundreds of churches, all these missions breathing fire and brimstone, telling you how easy it was to sin, how you'd be in hell. We were brainwashed into believing.' When he lost his faith, at the age of 17, it came as a relief. 'My whole life changed. If you haven't any doubts, you've no brain.'

Even so, something in him responded to his Jesuit education and it still informs many of his attitudes - duty and control are his watchwords - that I would not rule out a return to the fold. 'Well, people do tend to come back when they're looking for the exit,' he mutters.

He married Helen, a house model for Balmain, in 1965. The two of them were virgins on their wedding night. 'This idea that we were deprived of sex!' he yelps, when I express amazement at this. 'Romance is predicated on the non-fulfilment of the sexual urge. The frisson of non-fulfilment is probably more exciting than sex. I'd be hopeless, nowadays. Things are too confrontational. I could never take to promiscuity. I'm too fastidious. Anything used to put me off. Anything! Oh, God! Ugh! Ugh!' He sounds quite shrill. 'Women think that men will take anything going. No, they won't.' But when he married, didn't he hear a door slamming? Didn't he mourn all the women that might have been? 'No, I wouldn't have. I could never... no... no ! I couldn't have done. It was right for me to get married.'

The Wogans have two sons and a daughter (their first baby, Vanessa, had heart problems and never came home from hospital) and the family is, he tells me, the reason for everything he ever does. Is he easy to live with? 'We're careful of each other. The things that we argue about are so small and inconsequential, like, "Where are me socks?" or, "These handkerchiefs are dirty." We never shout at each other for more than 10 seconds and then we regret it. She's a great cook and she's very kind, gentle and loving.' Very softly, he adds: 'I think she's the best person I've ever met.'

Wogan's career, or so he maintains, was a kind of happy accident. After he left school, he spent five years working for the Royal Bank of Ireland, the permanent pensionable position his parents had always dreamed of for him. Then at 21, he entered, and won, a competition to become an announcer for the Irish station, RTE. Finally, in 1969, after two years doing Late Night Extra on Radio 1, for which he used to fly over from Dublin, he came to London as holiday cover for Jimmy Young and stayed.

'I was never really ambitious,' he says. 'I was never good at knocking on doors. I make it up as I go along.' Perhaps because of this insouciance, which may - who knows? - mask insecurity, he has never let success go to his head (others have hinted that he is being disingenuous when he says this, but I have an ego detector like you wouldn't believe and in his presence it didn't bleep once).

'People who are successful should never forget that it's 90 per cent luck. You've got to be an eejit to be an egomaniac. I had my glory years - Blankety Blank, the talk show, when I was winning every award going. But now half the population doesn't know who I am.'

Unsurprisingly, the stars he interviewed during the decade he presented Wogan used to drive him up the wall. It wasn't just drunk George Best and grumpy Prince Philip who were a problem; the professionals made his blood boil, too. Take Anne Bancroft. She appeared in his dressing room in tears; she hadn't realised the programme was live. She went on to answer only 'yes' and 'no' to all his questions, which didn't exactly make for riveting television.

Then there were the cases when guests had obviously taken drugs. 'I used to get furious inside. I'm not a great fan of anybody, so I'd be looking at them... ' His face is congested with disdain. 'You get a bloody actor who's on an upper or a downer - too far over the top because he's taken something up his nose or another pill - and you think: why come on the show if you don't want to talk? Idiot.'

Wogan has now been presenting the Radio 2 breakfast show, mark two, for 11 years; he has worked at the BBC, in one guise or another, for nearly 40. These days, however, he fears for its future. 'Morale is not good. As for the preposterous idea of funding it through voluntary contributions; if that ever came to pass, it would be dreadful. If they take away the licence fee, it'll all over.' His prescription, for the time being, is for the corporation to err on the side of quality.

'This extraordinary mantra of appealing to "yoof", as if youth were a specific section of society that never grows older.' Is Chris Moyles, the swollen loudmouth who presents the Radio 1 breakfast show, an example of what he means? In the past, the two have slagged one another off. 'Ye-es. But we don't know each other at all. Chris has got an Irish mother. He respects me, I respect him.' Hmm.

He cannot stand reality TV. 'They can only go one way with that. It's got to get seamier and seamier. Eventually, we'll end up with soft porn.' The other day, he had to interview the pre-operative transsexual who is the star of a reality show on Sky One called There's Something About Miriam (men were asked to compete for her affections without being told that 'she' was in fact a 'he'). 'It's called I'm Miriam, Come and Get Me! or something,' he splutters. 'How low can you go? Footballers' Wives! I've never seen anything like it! Nip/Tuck! It's got nothing to do with plastic surgery - it's all about bonking. How did we get to this? But perhaps I am an old fart... '

Suddenly, he is back to pondering his retirement. 'When is enough?' he says. 'Alistair Cooke, with the greatest respect, went on 10 years too long. Jimmy Young left under a cloud, which was a great pity. Ah, to be able to recognise when the tide is going out, when to get off the beach.'

I am just starting to worry about him when distraction arrives in the form of a fan. She has Elnet hair and pink lips and a nice line in lilac lambswool. 'Ooh, Terry,' she gasps, grabbing him by both elbows. 'Me and my friend are having a lovely day. We saw you doing the show and now we're having a spot of lunch.' She looks at me. 'Sorry to interrupt,' she says, though she clearly isn't sorry at all. Terry springs up, kisses her twice and signs an autograph.

Only once she has disappeared into the restaurant does he lower himself back into his seat. 'A groupie!' I chirrup, encouragingly. 'Ah, yes, I have a strange effect on old women,' he replies, all smiles.

Wogan on his guests

Dressed from head to toe in a turquoise shellsuit, David Icke claimed he was the Son of God. 'Why you?' asked an incredulous Wogan. 'People would have said the same thing to Jesus,' Icke replied. As the audience dissolved, Icke insisted: 'The best way of removing negativity is to laugh and be joyous, Terry.' 'But they're laughing at you,' said Wogan, 'they're not laughing with you.'

George Best got drunk in the hospitality suite before appearing and proceeded to ring out a string of swear words. He then kissed Omar Sharif, the other guest on the show. Viewers flooded the station with complaints. 'Let's just say his communication skills weren't working too well that day,' said Wogan. 'We were only supposed to have about eight or nine million viewers but everyone in Britain seemed to be watching.'

David Bowie nearly provoked violence. 'I didn't hit him, but it came close. For reasons best known to him, he came on unwilling to talk.'

'Bette Davis was a real hero of mine who I'd been really looking forward to having on the show. But she was a right pain because we didn't mention her book in the first sentence and she was cross about it.'

The critics on Wogan

According to the Guardian: 'Wogan was so star-struck when he met Madonna [below] he made Jonathan Ross's effort, itself in the first rank of sycophancy, look like Jeremy Paxman with piles.'

Victor Lewis-Smith: 'He's never invaded Poland, of course, nor (to the best of my knowledge) has he ever set fire to the Reichstag, but his annual contribution to the Eurovision Song Contest has surely done (in peacetime) for European brotherhood what the Third Reich only achieved by war.'